a) Use a correct method to express $\overrightarrow {OP} $ in terms of $\lambda $

Obtain the given answer

b) EITHER: Use correct method to express scalar product of $\overrightarrow {OA} $ and $\overrightarrow {OP} $, or $\overrightarrow {OB} $ and $\overrightarrow {OP} $ in terms of $\lambda $

Using the correct method for the moduli, divide scalar products by products of moduli and express $\cos AOP = \cos BOP$ in terms of $\lambda $, or in terms of $\lambda $ and $OP$

OR1: Use correct method to express $O{A^2} + O{P^2} - A{P^2}$, or $O{B^2} + O{P^2} - B{P^2}$ in terms of $\lambda $

Using the correct method for the moduli, divide each expression by twice the product of the relevant moduli and express $\cos AOP = \cos BOP$ in terms of $\lambda $, or $\lambda $ and $OP$

Obtain a correct equation in any form, e.g. $\frac{{9 + 2\lambda }}{{3\sqrt {\left( {9 + 4\lambda  + 12{\lambda ^2}} \right)} }} = \frac{{11 + 14\lambda }}{{5\sqrt {\left( {9 + 4\lambda  + 12{\lambda ^2}} \right)} }}$

Solve for $\lambda $

Obtain $\lambda  = \frac{3}{8}$

c) Verify the given statement correctly